If the user intends to establish 95% confidence interval for comparison with other correlation coefficients, or to use the
results in a future meta-analysis, then a two tail model is appropriate.

More commonly, however, the interest is whether a significant correlation exists in the data observed, whether one
of the tails overlaps
the null value of zero (0). In this case, the one tail model suffices, and requires a smaller sample size.

In most publications, therefore, when the one or two tail model is not mentioned, the default is usually the one tail model.

Example

To establish an expected correlation coefficient (ρ) of 0.6, significant at the α<0.05 and a power (1-β)
of 0.8, requires 16 pairs of x/y values, taking the default position of a one tail model.